On a class of singular hyperbolic equation with a weighted integral condition

Said Mesloub,Abdelfatah Bouziani

doi:10.1155/s0161171299225112

Abstract

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

Highlights

Problem (1.1), (1.2), and (1.3) can be viewed as a nonlocal boundary problem for a singular hyperbolic equation
From the inequality (3.1), it follows that the operator L has an inverse and, from Corollary 2, we deduce that the range R(L) of the operator L is closed
Relation (4.2) is given for any function u ∈ D0(L), so we can express it in the following particular form: Let utt be the solution of the equation utt −

Summary

Introduction

Problem (1.1), (1.2), and (1.3) can be viewed as a nonlocal boundary problem for a singular hyperbolic equation. We prove the existence, uniqueness and continuous dependence upon the data of a strong solution of problem (1.1), (1.2), and (1.3). For the investigation of the posed problem, we need some function spaces.

Results

Conclusion